FRANKFURT/LONDON, March 9 (Reuters) - European steelmakers are pinning their hopes on the European Union being able to negotiate an exemption from new U.S. steel import tariffs that have raised fears of a damaging trade war

Share prices initially fell across the European steel sector on Friday, but there was something of a mixed picture, with two of the blocs biggest producers saying the move will have limited impact on them.

U.S. President Donald Trump announced import tariffs of 25 percent on steel and 10 percent on aluminium on Thursday, exempting Canada and Mexico while offering the possibility of excluding other allies.

The European Union responded by saying it would ask the World Trade Organization to impose its own measures, adding that it was hopeful the bloc would be made exempt.

Europe is the biggest exporter of steel to the United States, accounting for nearly 5 million tonnes out of total U.S. imports of about 35 million tonnes a year.

European steel industry body Eurofer issued a statement saying that the U.S. decision was "damaging and counterproductive for both the U.S. and EU economies".

"The concern for EU steel producers is not only the potential loss of access to a market with which they have strong commercial links, but even more that trade deflection towards the EU's open market will be large and sudden," said Eurofer Director General Axel Eggert.

Shares in ArcelorMittal, Europe's biggest steelmaker, were down 0.6 percent at 1635 GMT, while India's Tata Steel fell by 4.6 percent. The U.S. represents about 10 percent of Tata Steel Europe's sales, an industry source said.

Salzgitter (SZGG.DE), Germanys second-largest steelmaker, was down 5.7 percent. The group did not respond to requests for comment, but its CEO said on Thursday that markets were overestimating the impact of the tariffs on its business.

German industry body BDI echoed Eurofer's concerns over redirected steel flows but said it was asking for moderation to avoid stoking a trade war.

"A new wave of protectionist measures would quickly hit Germany," said BDI President Dieter Kempf, adding that about one in every four jobs in Germany depends on exports.

The German steel industry is dominated by Thyssenkrupp , which said it supplies between 400,000 and 500,000 tonnes of steel a year to the United States. The company's shares were in positive territory with a gain of 0.6 percent.

MIXED IMPACT

The volumes of steel imported by the United States, with Canada, Brazil and South Korea among the leading suppliers, represented less than 8 percent of the 473 million tonnes of steel traded globally last year.

Consultancy Wood Mackenzie expects the U.S. tariffs to displace a maximum of 18 million tonnes of steel, less than 4 percent of annual traded volumes.

Austria's Voestalpine, regarded as among the world's most efficient steelmakers, said it might not invest further in the United States until the political environment is clear.

The company said that a maximum of about 3 percent of its sales could be affected by the tariffs and that the economic risk remains very manageable, even in extreme cases, though it expects further exemptions to be agreed by the United States. Shares in the company rose by 1.5 percent.

Ratings agency Moody's has said that the tariffs are credit-negative for European steelmakers.

For companies that have operations in the United States, the impact could be mixed.

Swedish steelmaker SSAB said it expected a two-fold impact from the U.S. tariffs, with a negative impact in Europe, where it generates most of its sales, mitigated by a positive impact in the United States, where it is one of the largest steel plate producers. Its shares were down 3 percent in late afternoon trade..

Finland's Outokumpu, meanwhile, said it expects a slightly positive overall impact because of its operations in the United States and Mexico, though its share price still dipped by 1.2 percent.

The Thomson Reuters Europe Steel Index, which had slumped by 4.6 percent after Trump's announcement on Thursday, recovered some of those losses with a 1.3 percent gain on Friday, though investors will be watching developments closely in the coming days and weeks.

For mining companies that produce the bauxite and iron ore used in aluminium and steel manufacture, anything that hampers free trade tends to be unwelcome.

"All other things being equal, increased tariffs are not welcome because they will hurt poorer countries harder and impede their development," said Tom Butler, CEO of the International Council of Mining and Metals industry body.

(Additional reporting by Michael Shields in Zurich, Tom Kaeckenhoff in Duesseldorf, Anna Stablum in Stockholm, Jussi Rosendahl in Helsinki and Barbara Lewis in London Editing by Alexander Smith and David Goodman)